The objective of this work is to develop a new approach to multichannel fluorescence spectroscopy that will result in extended sensitivity for a number of imaging applications in biomedical research, including high-speed multiplexed read-out of bio-chips, rapid DNA sequencing, fluorescence lifetime imaging microscopy, and cell imaging experiments that require separation of fluorescent labels with overlapping excitation and/or emission spectra, such as green fluorescent protein and its variations. The aims include implementation of a scanning confocal microscope with multiple excitation wavelengths, multiple emission wavelength bands, and time-resolved single-photon detection, and also implementation of statistically efficient maximum-likelihood based methods for the resolution of the resultant multi-channel data sets into the fractional components corresponding to each fluorophore present, and background. Numerical methods will be used to solve the analytically intractable maximum-likelihood equations to determine the component fractions and their errors and co-dependence. Analysis software will be made available for internet download. Also, a procedure will be developed for the optimal selection of the excitation wavelengths and emission bands for given fluorophores and experimental conditions. The maximum-likelihood based approach will be evaluated using experimental test data. Monte Carlo simulations will also be developed to validate the new approach using the spectra of commonly-used fluorophores and to determine its capabilities in terms of the accuracy (lack of bias), statistical precision, and covariance of parameters for given signal and background levels, particularly for photon-starved imaging applications. The performance range of the maximum-likelihood based approached will be compared with that of existing least-squares curve-fitting-based "linear un-mixing", which is expected to become statistically invalid for low-count data sets.